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It sounds like the fuel rail is losing pressure overnight. I would put a pressure gage on it overnight and see what it is at in the morning.
If it is losing pressure the 2 suspects are the pressure regulator valve or the umbrella valve at the fuel pump assembly.
2 seconds at start up is not enough to bring the rail up to pressure from 0 psi. If I remember correctly the fuel pump is turned on KOER by the oil pressure switch. So after he cranks it a bit the oil pressure comes up and the pump stays on and finally pressurizes the rail.
Just a lil tis bit from my experience I have a 02, and at about 35,000 a relay went out in the fuel system. And that is what mine did for a while it wouldent start, then it would. but thats just my little opinion!